Effects of Noncommutativity on Light Hydrogen-Like Atoms and Proton Radius

Abstract

We study the corrections induced by the theory of non-commutativity, in both space-space and space-time versions, on the spectrum of hydrogenlike atoms. For this, we use the relativistic theory of two-particle systems to take into account the effects of the reduced mass, and we use perturbation methods to study the effects of non-commutativity.We apply our study to the muon hydrogen with the aim to solve the puzzle of proton radius [R. Pohl et al., Nature 466, 213 (2010) and A. Antognini et al., Science 339, 417 (2013)]. The shifts in the spectrum are found more noticeable in muon H (µH) than in electron H (eH) because the corrections depend on the mass to the third power; This explains the discrepancy between µH and eH results. In space-space non-commutativity, the parameter required to resolve the puzzle θss ≈ (0.35GeV ) −2 , exceeds the limit obtained for this parameter from various studies on eH Lamb shift. For space-time non-commutativity, the value θst ≈ (14.3GeV ) −2 has been obtained and it is in agreement with the limit determined by Lamb shift spectroscopy in eH. We have also found that this value fills the gap between theory and experiment in the case of µD and improves the agreement between theoretical and experimental values in the case of hydrogen-deuterium isotope shift.

Hydrogen and muonic hydrogen atomic spectra in non-commutative space-time

“…Equation (9) for θ 0i = 0 and θ i j = 0, has been already considered to find bound on the NC-parameter in hydrogen atom [71,[73][74][75]. The temporal part of the non-commutativity leads to a problem with the unitarity.…”

“…Here we would like to study the two-body bound state in non-commutative space to explore the differences in the electronic and muonic hydrogen spectrum. There are many studies on the hydrogen atom in the NC space-time [70][71][72][73][74][75][76][77][78][79][80]. However, the effect of NC space on the hydrogen atom at the lowest order is doubtful.…”

$\mathcal{O} \,(θ)$ Feynman rules for quadrilinear gauge boson couplings in noncommutative standard model

“…Over the last 15 years, there has been an increasing interest to study noncommutative standard model as a candidate for beyond Glashaw, Weinberg and Salam model of particle physics [1][2][3][4][5][6][7][8]. This is partially because of the modern foundations of string theory, where in its context it was shown that noncommutative models occur in description of low energy excitations of open strings in the presence of a constant background B-field [9].…”